Mrs.D Math · 7th Grade

SPACE
EXPLORER

Sample Space
S = { all outcomes }
List every possibility
Order matters!
📝 List It
🔢 Count It
🧮 Find It
📝 List It
🔢 Count It
🧮 Find P(event)
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📚 Sample Space

What is a Sample Space?

A sample space is the set of ALL possible outcomes of an experiment. We write it as S = {outcome1, outcome2, ...}

1
Flip a coin: S = {H, T} — two possible outcomes.
Always list every outcome exactly once
2
Roll a die: S = {1, 2, 3, 4, 5, 6} — six possible outcomes.
3
Flip a coin AND roll a die: Combine each coin outcome with each die outcome.
S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6} — 12 outcomes

Counting Outcomes — Shortcut

×
Multiply the number of outcomes for each action.
Coin (2) × Die (6) = 12 total outcomes
×
Two coins: 2 × 2 = 4  |  Three coins: 2 × 2 × 2 = 8
S = {HH, HT, TH, TT} for two coins

Using Sample Space for Probability

Once you have the sample space, finding probability is easy:

P
P(event) = favorable outcomes in S ÷ total outcomes in S
S = {H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6} → P(heads) = 6/12 = 1/2
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